Midfielder Kris Commons, who shrugged off a nasty ankle injury to make the game, drove the home side into the lead in the 14th minute and then grabbed a poacher's second the 51st minute before defender Mikael Lustig grabbed the third just after the hour mark.
With closest challengers Motherwell drawing 2-2 at home with St Mirren it means Celtic, with five games remaining after the split, go 15 points clear with a massive goal advantage and while there is no doubt about the destination of the title, Hoops fans will have to wait a bit longer before it is official.
Celtic manager Neil Lennon had wanted to see some swagger from his side and to that end he made two changes.
Midfielder Victor Wanyama's appeal against last week's red card at St Mirren allowed him to play but Georgios Samaras and Beram Kayal dropped to the bench to be replaced by Lustig and Anthony Stokes.
For Hibs, who had not lost to Celtic in two previous SPL meetings this season, Paul Hanlon was back in defence after recovering from a hip injury.
Jorge Claros and David Wotherspoon were brought back in, with Lewis Stevenson and Eoin Doyle on the bench and Tom Taiwo out altogether.
Given the circumstances, Celtic Park was surprisingly far from full and in the fifth minute the home fans collectively held their breath as Leigh Griffiths' inviting ball from a free-kick was missed by everyone before skipping past Fraser Forster's far post.
The home side took their time to get up to speed but in the 12th minute Commons' low drive from outside the box was the first test for Hibs keeper Ben Williams who saved with a degree of ease.
The Scotland midfielder, however, was more convincing two minutes later when he confidently drove the Parkhead side ahead.
Striker Gary Hooper took a pass from Charlie Mulgrew and laid the ball off to Commons who shrugged off the attention of Hanlon inside the box to drill the ball low past Williams and into the corner of the net.
The goal established Celtic's control and thereafter they pressed the reticent visitors back towards their own penalty area.
A fine moving involving Hooper and Stokes ended with the Irishman setting up Mulgrew on the left-hand side of the box but the Hoops midfielder was unusually hesitant on his trusty left foot, allowing Hibs defender Tim Clancy to block the delayed shot.
Moments later Hooper broke through the Hibs defence to take a return pass from Stokes but his finish from eight yards lacked the power to beat Williams.
Stokes had a decent chance three minutes into the second-half after Wanyama played in Joe Ledley, whose cross was dummied perfectly for the former Hibs player but he failed to catch his shot properly and the ball bounced through to Williams.
Three minutes later Commons showed him how it should be done when he doubled Celtic's lead.
Wanyama played the ball to the supporting Lustig and when his cut-back found the former Derby and Nottingham Forest player he turned smartly from seven yards out and knocked it low past Williams. With that convincing finish the three points appeared secure.
Five minutes later Commons was presented with a chance for a hat-trick after Claros was robbed by Hooper in his own box but his pass caught his team-mate off-balance and the ball bobbled behind.
But it looked like it was a matter of how many the home side would score and in the 61st minute Lustig made it 3-0 from Ledley's cross. The Hibs players claimed the ball came off his arm on the way through but the strike stood.
From that point it became party time for the home fans as they listened for news from Motherwell and when word that St Mirren had come from one behind to go 2-1 up, the decibel levels increased.
But a late equaliser at Fir Park ensured the title race, if it can be called that, will go on.
- Sports & Recreation
- Mikael Lustig
- St Mirren
- Kris Commons